(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     32626,       1067]
NotebookOptionsPosition[     27414,        873]
NotebookOutlinePosition[     27832,        889]
CellTagsIndexPosition[     27789,        886]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[TextData[{
 "New in: ",
 Cell["0.0", "HistoryData",
  CellTags->"New"],
 " | Modified in: ",
 Cell[" ", "HistoryData",
  CellTags->"Modified"],
 " | Obsolete in: ",
 Cell[" ", "HistoryData",
  CellTags->"Obsolete"],
 " | Excised in: ",
 Cell[" ", "HistoryData",
  CellTags->"Excised"]
}], "History",
 CellID->1247902091],

Cell[CellGroupData[{

Cell["Categorization", "CategorizationSection",
 CellID->1122911449],

Cell["Tutorial", "Categorization",
 CellLabel->"Entity Type",
 CellID->686433507],

Cell["MathMR", "Categorization",
 CellLabel->"Paclet Name",
 CellID->605800465],

Cell["MathMR`", "Categorization",
 CellLabel->"Context",
 CellID->468444828],

Cell["MathMR/tutorial/NVInteraction", "Categorization",
 CellLabel->"URI"]
}, Closed]],

Cell[CellGroupData[{

Cell["Keywords", "KeywordsSection",
 CellID->1427428552],

Cell["XXXX", "Keywords",
 CellID->1251852827]
}, Closed]],

Cell[CellGroupData[{

Cell["Details", "DetailsSection",
 CellID->307771771],

Cell["XXXX", "Details",
 CellLabel->"Lead",
 CellID->218895918],

Cell["XXXX", "Details",
 CellLabel->"Developers",
 CellID->350963985],

Cell["XXXX", "Details",
 CellLabel->"Authors",
 CellID->795871300],

Cell["XXXX", "Details",
 CellLabel->"Feature Name",
 CellID->199739161],

Cell["XXXX", "Details",
 CellLabel->"QA",
 CellID->40625308],

Cell["XXXX", "Details",
 CellLabel->"DA",
 CellID->357121918],

Cell["XXXX", "Details",
 CellLabel->"Docs",
 CellID->35949532],

Cell["XXXX", "Details",
 CellLabel->"Features Page Notes",
 CellID->929432370],

Cell["XXXX", "Details",
 CellLabel->"Comments",
 CellID->240026365]
}, Closed]],

Cell[CellGroupData[{

Cell["NVInteraction", "Title",
 CellID->509267359],

Cell["\<\
In this tutorial, the interactions of NV center system in diamond \
demonstrated.\
\>", "Text",
 CellChangeTimes->{{3.498708633609289*^9, 3.498708667230931*^9}},
 CellID->1534169418],

Cell[BoxData[GridBox[{
   {
    ButtonBox["MagBFrame",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/MagBFrame"], Cell[
    "The coordinate system defined by the applied magnetic field", 
     "TableText"]},
   {
    ButtonBox["MagneticBDirection",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/MagneticBDirection"], Cell["\<\
calculate the B directin in the Cartesian coordinate system\
\>", "TableText"]},
   {
    RowBox[{"$e1", ",", "$e2", ",", "$e3"}], Cell[
    "Basis of Cartesian coordiante system", "TableText"]},
   {
    RowBox[{"$Xdir", ",", "$Ydir", ",", "$Zdir"}], 
    RowBox[{
    "Basis", " ", "of", " ", "intrinsic", " ", "coordinate", " ", "system"}]}
  }]], "DefinitionBox",
 CellChangeTimes->{{3.498708605348328*^9, 3.498708620464747*^9}, {
  3.498708692366391*^9, 3.498708876162223*^9}},
 CellID->2096742444],

Cell["Coordinate system", "Caption",
 CellChangeTimes->{{3.498708961698875*^9, 3.498708964681724*^9}},
 CellID->1891092685],

Cell[CellGroupData[{

Cell["\<\
Three kind of basis are defined here: natural Cartesian, intrisic, and \
magnetic frame\
\>", "MathCaption",
 CellChangeTimes->{{3.498708888353115*^9, 3.498708917452132*^9}},
 CellID->836781195],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"$e1", ",", "$e2", ",", "$e3"}], "}"}]], "Input",
 CellChangeTimes->{{3.498708758343057*^9, 3.498708781158919*^9}},
 CellLabel->"In[8]:=",
 CellID->201251739],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.498708759968019*^9, 3.498708781678551*^9}},
 CellLabel->"Out[8]=",
 CellID->1297040926]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"$Xdir", ",", "$Ydir", ",", "$Zdir"}], "}"}]], "Input",
 CellChangeTimes->{{3.498708856610032*^9, 3.498708864433414*^9}},
 CellLabel->"In[9]:=",
 CellID->1686696713],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     FractionBox["1", 
      SqrtBox["2"]], ",", 
     RowBox[{"-", 
      FractionBox["1", 
       SqrtBox["2"]]}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["1", 
      SqrtBox["6"]], ",", 
     FractionBox["1", 
      SqrtBox["6"]], ",", 
     RowBox[{"-", 
      SqrtBox[
       FractionBox["2", "3"]]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["1", 
      SqrtBox["3"]], ",", 
     FractionBox["1", 
      SqrtBox["3"]], ",", 
     FractionBox["1", 
      SqrtBox["3"]]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.498708864987242*^9},
 CellLabel->"Out[9]=",
 CellID->1379868343]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MagBFrame", "[", 
  RowBox[{
   RowBox[{"45.", "Degree"}], ",", 
   RowBox[{"10.", "Degree"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.498708921859157*^9, 3.498708948016467*^9}},
 CellLabel->"In[11]:=",
 CellID->1089850160],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0.13428349710238624`", ",", 
     RowBox[{"-", "0.850524255909822`"}], ",", 
     RowBox[{"-", "0.5085041125841532`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.2792582776338194`", ",", "0.524833885571765`", ",", 
     RowBox[{"-", "0.8040921632055843`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.9507800780301121`", ",", 
     RowBox[{"-", "0.0340276749820958`"}], ",", "0.3079924683435729`"}], 
    "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.49870894064611*^9, 3.498708948277826*^9}},
 CellLabel->"Out[11]=",
 CellID->2143837741]
}, Open  ]]
}, Open  ]],

Cell[BoxData[GridBox[{
   {
    ButtonBox["QubitHami",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/QubitHami"], 
    RowBox[{"Ground", " ", "state", " ", "spin", " ", "Hamiltonian"}]},
   {
    ButtonBox["ExcitedStateHami",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/ExcitedStateHami"], 
    RowBox[{"Excited", " ", "state", " ", "spin", " ", "Hamiltonian"}]},
   {
    ButtonBox["Eigen",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/Eigen"], 
    RowBox[{"Eigensystem", " ", "of", " ", "ground", " ", "state", " "}]},
   {
    ButtonBox["ExcitedStateEigen",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/ExcitedStateEigen"], 
    RowBox[{"Eigensystem", " ", "of", " ", "excited", " ", "state", " "}]},
   {
    ButtonBox["Svalue",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/Svalue"], 
    RowBox[{
    "Mean", " ", "spin", " ", "values", " ", "of", " ", "ground", " ", 
     "state"}]}
  }]], "DefinitionBox",
 CellChangeTimes->{{3.498708605348328*^9, 3.498708620464747*^9}, {
  3.498708692366391*^9, 3.498708876162223*^9}, {3.498708989135444*^9, 
  3.498709146912191*^9}},
 CellID->295055199],

Cell["Central NV spin state", "Caption",
 CellChangeTimes->{{3.498708961698875*^9, 3.498708982249035*^9}},
 CellID->879203334],

Cell[CellGroupData[{

Cell["\<\
The Hamiltonian of ground state and excited state spins as functions of \
magnetic field\
\>", "MathCaption",
 CellChangeTimes->{{3.498708888353115*^9, 3.498708917452132*^9}, {
  3.498709157993625*^9, 3.498709179263984*^9}},
 CellID->874840856],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"QubitHami", "[", 
   RowBox[{"0.0500", ",", 
    RowBox[{"45.", "Degree"}], ",", 
    RowBox[{"10.", "Degree"}]}], "]"}], "//", "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.498709186730898*^9, 3.498709198217247*^9}},
 CellLabel->"In[13]:=",
 CellID->723392520],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1.8791682481229746`", 
      RowBox[{
       RowBox[{"-", "0.6899798001807982`"}], "+", 
       RowBox[{"0.12166205491571012`", " ", "\[ImaginaryI]"}]}], "0"},
     {
      RowBox[{
       RowBox[{"-", "0.6899798001807982`"}], "-", 
       RowBox[{"0.12166205491571012`", " ", "\[ImaginaryI]"}]}], "0", 
      RowBox[{
       RowBox[{"-", "0.6899798001807982`"}], "+", 
       RowBox[{"0.12166205491571012`", " ", "\[ImaginaryI]"}]}]},
     {"0", 
      RowBox[{
       RowBox[{"-", "0.6899798001807982`"}], "-", 
       RowBox[{"0.12166205491571012`", " ", "\[ImaginaryI]"}]}], 
      "3.8608317518770257`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.498709194580792*^9, 3.498709198639097*^9}},
 CellLabel->"Out[13]//MatrixForm=",
 CellID->303982011]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"ExcitedStateHami", "[", 
   RowBox[{"0.0500", ",", 
    RowBox[{"45.", "Degree"}], ",", 
    RowBox[{"10.", "Degree"}], ",", "1.0"}], "]"}], "//", 
  "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.498709208064794*^9, 3.498709214925904*^9}},
 CellLabel->"In[15]:=",
 CellID->1141463959],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0.40916824812297425`", 
      RowBox[{
       RowBox[{"-", "0.6899798001807982`"}], "+", 
       RowBox[{"0.12166205491571012`", " ", "\[ImaginaryI]"}]}], "1.`"},
     {
      RowBox[{
       RowBox[{"-", "0.6899798001807982`"}], "-", 
       RowBox[{"0.12166205491571012`", " ", "\[ImaginaryI]"}]}], "0", 
      RowBox[{
       RowBox[{"-", "0.6899798001807982`"}], "+", 
       RowBox[{"0.12166205491571012`", " ", "\[ImaginaryI]"}]}]},
     {"1.`", 
      RowBox[{
       RowBox[{"-", "0.6899798001807982`"}], "-", 
       RowBox[{"0.12166205491571012`", " ", "\[ImaginaryI]"}]}], 
      "2.3908317518770255`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.498709208444931*^9, 3.498709215720553*^9}},
 CellLabel->"Out[15]//MatrixForm=",
 CellID->285172659]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["There eigen-systems", "MathCaption",
 CellChangeTimes->{{3.498708888353115*^9, 3.498708917452132*^9}, {
  3.498709157993625*^9, 3.498709179263984*^9}, {3.498709232798478*^9, 
  3.49870924262923*^9}},
 CellID->1520014403],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Eigen", "[", 
  RowBox[{"0.0500", ",", 
   RowBox[{"45.", "Degree"}], ",", 
   RowBox[{"10.", "Degree"}]}], "]"}]], "Input",
 CellChangeTimes->{3.498709253937296*^9},
 CellLabel->"In[16]:=",
 CellID->1940946482],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"-", "0.33826953366642376`"}], "+", 
      RowBox[{"2.7317696112123083`*^-18", " ", "\[ImaginaryI]"}]}], ",", 
     RowBox[{"2.086852323764151`", "\[InvisibleSpace]", "-", 
      RowBox[{"1.0139148244363166`*^-18", " ", "\[ImaginaryI]"}]}], ",", 
     RowBox[{"3.991417209902273`", "\[InvisibleSpace]", "-", 
      RowBox[{"2.237624597118073`*^-16", " ", "\[ImaginaryI]"}]}]}], "}"}], 
   ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"0.2930176690839961`", "\[InvisibleSpace]", "-", 
        RowBox[{"0.05166692088381315`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{"0.9416919886472918`", "\[InvisibleSpace]", "+", 
        RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{"0.15473512210711676`", "\[InvisibleSpace]", "+", 
        RowBox[{"0.027283976890703554`", " ", "\[ImaginaryI]"}]}]}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"0.952780672470656`", "\[InvisibleSpace]", "+", 
        RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{
        RowBox[{"-", "0.2781395053989935`"}], "-", 
        RowBox[{"0.049043499202750314`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{
        RowBox[{"-", "0.10481739783314374`"}], "-", 
        RowBox[{"0.03815041284450306`", " ", "\[ImaginaryI]"}]}]}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"0.05700585517848821`", "\[InvisibleSpace]", "-", 
        RowBox[{"0.020748434463859544`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{
        RowBox[{"-", "0.18011309765068736`"}], "+", 
        RowBox[{"0.031758798694794595`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{"0.9812596423489582`", "\[InvisibleSpace]", "+", 
        RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]}], "}"}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.498709254690903*^9},
 CellLabel->"Out[16]=",
 CellID->706670819]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ExcitedStateEigen", "[", 
  RowBox[{"0.0500", ",", 
   RowBox[{"45.", "Degree"}], ",", 
   RowBox[{"10.", "Degree"}], ",", "1.0"}], "]"}]], "Input",
 CellChangeTimes->{{3.498709270279725*^9, 3.498709270617111*^9}},
 CellLabel->"In[17]:=",
 CellID->1668430510],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"-", "0.5467851948730407`"}], "-", 
      RowBox[{"6.011204575305903`*^-17", " ", "\[ImaginaryI]"}]}], ",", 
     RowBox[{"0.2684850164071235`", "\[InvisibleSpace]", "-", 
      RowBox[{"2.4520210954303087`*^-17", " ", "\[ImaginaryI]"}]}], ",", 
     RowBox[{"3.078300178465917`", "\[InvisibleSpace]", "+", 
      RowBox[{"4.299889328391874`*^-17", " ", "\[ImaginaryI]"}]}]}], "}"}], 
   ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"0.5783199249473697`", "\[InvisibleSpace]", "-", 
        RowBox[{"0.20722992397408893`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{"0.782197335563575`", "\[InvisibleSpace]", "+", 
        RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{
        RowBox[{"-", "0.013146562112526905`"}], "+", 
        RowBox[{"0.10293842412057491`", " ", "\[ImaginaryI]"}]}]}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"0.6804637587327874`", "\[InvisibleSpace]", "+", 
        RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{
        RowBox[{"-", "0.49679715328532326`"}], "-", 
        RowBox[{"0.24369799249096807`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{
        RowBox[{"-", "0.4681586397435247`"}], "-", 
        RowBox[{"0.10770532961841234`", " ", "\[ImaginaryI]"}]}]}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"0.3990146626628559`", "\[InvisibleSpace]", "-", 
        RowBox[{"0.018926041579161668`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{
        RowBox[{"-", "0.28538948943946063`"}], "+", 
        RowBox[{"0.022892018220315467`", " ", "\[ImaginaryI]"}]}], ",", 
       RowBox[{"0.870894883869159`", "\[InvisibleSpace]", "+", 
        RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]}], "}"}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.49870927099592*^9},
 CellLabel->"Out[17]=",
 CellID->729389960]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["The mean value of spin components for a given state", "MathCaption",
 CellChangeTimes->{{3.498708888353115*^9, 3.498708917452132*^9}, {
  3.498709157993625*^9, 3.498709179263984*^9}, {3.498709232798478*^9, 
  3.49870924262923*^9}, {3.498709286580138*^9, 3.498709300562607*^9}},
 CellID->857902880],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Svalue", "[", 
  RowBox[{"1", ",", "0.0500", ",", 
   RowBox[{"45.", "Degree"}], ",", 
   RowBox[{"10.", "Degree"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.498709305157443*^9, 3.498709310422951*^9}},
 CellLabel->"In[18]:=",
 CellID->2042472293],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.5014286032132954`", ",", 
   RowBox[{"-", "0.34186182950497385`"}], ",", 
   RowBox[{"-", "0.04899013573400464`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.498709311209812*^9},
 CellLabel->"Out[18]=",
 CellID->1551133660]
}, Open  ]]
}, Open  ]],

Cell[BoxData[GridBox[{
   {
    ButtonBox["HyperfineField",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/HyperfineField"], 
    RowBox[{
    "Hyperfine", " ", "interaction", " ", "between", " ", "electron", " ", 
     SuperscriptBox[
      RowBox[{"and", " "}], "13"], "C", " ", "spin"}]},
   {
    ButtonBox["DipolarInteraction",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/DipolarInteraction"], 
    RowBox[{"Dipolar", " ", "interaction", " ", "betwee", " ", 
     SuperscriptBox[
      RowBox[{"two", "  "}], "13"], "C", " ", "spins"}]},
   {
    ButtonBox["DipolarInteractionTable",
     BaseStyle->"Link",
     ButtonData->"paclet:MathMR/ref/DipolarInteractionTable"], 
    RowBox[{
    "Mutural", " ", "dipolar", " ", "interactions", " ", "of", " ", "a", " ", 
     "set", " ", "of", " ", "spins"}]}
  }]], "DefinitionBox",
 CellChangeTimes->{{3.498708605348328*^9, 3.498708620464747*^9}, {
  3.498708692366391*^9, 3.498708876162223*^9}, {3.498708989135444*^9, 
  3.498709146912191*^9}, {3.498709351063225*^9, 3.498709513905745*^9}, {
  3.49870954595786*^9, 3.498709546204166*^9}},
 CellID->609356121],

Cell["HF and dipolar interactions", "Caption",
 CellChangeTimes->{{3.498708961698875*^9, 3.498708982249035*^9}, {
  3.498709430893702*^9, 3.498709436492547*^9}},
 CellID->1087339240],

Cell[CellGroupData[{

Cell["The hyperfine interactions", "MathCaption",
 CellChangeTimes->{{3.498708888353115*^9, 3.498708917452132*^9}, {
  3.498709157993625*^9, 3.498709179263984*^9}, {3.498709232798478*^9, 
  3.49870924262923*^9}, {3.498709286580138*^9, 3.498709300562607*^9}, {
  3.498709482499308*^9, 3.498709487586169*^9}},
 CellID->1883277671],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"HyperfineField", "[", 
  RowBox[{
   RowBox[{"$DiamondLatticeConst", "*", 
    RowBox[{"{", 
     RowBox[{"3", ",", "3", ",", 
      RowBox[{"-", "1"}]}], "}"}]}], ",", "1", ",", "0.0100", ",", 
   RowBox[{"30", "Degree"}], ",", 
   RowBox[{"0.0", "Degree"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.498709305157443*^9, 3.498709310422951*^9}, 
   3.498709500602944*^9},
 CellLabel->"In[19]:=",
 CellID->1101951984],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "3.414025151549751`"}], ",", "0.023500332558288005`", ",", 
   RowBox[{"-", "1.9695363744363017`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.498709311209812*^9, 3.498709501206815*^9},
 CellLabel->"Out[19]=",
 CellID->816580272]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"exampleSval", "=", 
   RowBox[{"Svalue", "[", 
    RowBox[{"1", ",", "0.0100", ",", 
     RowBox[{"30", "Degree"}], ",", 
     RowBox[{"0.0", "Degree"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"HyperfineField", "[", 
  RowBox[{
   RowBox[{"$DiamondLatticeConst", "*", 
    RowBox[{"{", 
     RowBox[{"3", ",", "3", ",", 
      RowBox[{"-", "1"}]}], "}"}]}], ",", "exampleSval", ",", "0.0100", ",", 
   RowBox[{"30", "Degree"}], ",", 
   RowBox[{"0.0", "Degree"}]}], "]"}]}], "Input",
 CellLabel->"In[20]:=",
 CellID->2026486792],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "3.414025151549751`"}], ",", "0.023500332558288005`", ",", 
   RowBox[{"-", "1.9695363744363017`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.49870950657793*^9},
 CellLabel->"Out[21]=",
 CellID->1963445781]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["The dipolar interactions between two dimer spins", "MathCaption",
 CellChangeTimes->{{3.498708888353115*^9, 3.498708917452132*^9}, {
  3.498709157993625*^9, 3.498709179263984*^9}, {3.498709232798478*^9, 
  3.49870924262923*^9}, {3.498709286580138*^9, 3.498709300562607*^9}, {
  3.498709482499308*^9, 3.498709487586169*^9}, {3.498709523977418*^9, 
  3.498709537527895*^9}},
 CellID->42218018],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"examle2SpinCoord", "=", 
   RowBox[{"Spin2Cluster", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"1", ",", "3", ",", "1"}], "}"}], ",", "1", ",", "1"}], "]"}]}],
   ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"DipolarInteraction", "[", 
    RowBox[{
     RowBox[{
     "examle2SpinCoord", "\[LeftDoubleBracket]", "1", 
      "\[RightDoubleBracket]"}], ",", 
     RowBox[{
     "examle2SpinCoord", "\[LeftDoubleBracket]", "2", 
      "\[RightDoubleBracket]"}], ",", "1.0", ",", "0.0", ",", "0.0"}], "]"}], 
   "/", "2"}], "/", "\[Pi]"}]}], "Input",
 CellLabel->"In[22]:=",
 CellID->154343777],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"2.055524818973846`", ",", "2.055524818973846`", ",", 
   RowBox[{"-", "4.111049637947692`"}], ",", "3.325389312246021`*^-31", ",", 
   RowBox[{"-", "1.198097765399441`*^-15"}], ",", 
   "1.7115682362849156`*^-15"}], "}"}]], "Output",
 CellChangeTimes->{3.498709540607874*^9},
 CellLabel->"Out[23]=",
 CellID->104243093]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["The dipolar interactions between a set of spins", "MathCaption",
 CellChangeTimes->{{3.498708888353115*^9, 3.498708917452132*^9}, {
  3.498709157993625*^9, 3.498709179263984*^9}, {3.498709232798478*^9, 
  3.49870924262923*^9}, {3.498709286580138*^9, 3.498709300562607*^9}, {
  3.498709482499308*^9, 3.498709487586169*^9}, {3.498709523977418*^9, 
  3.498709537527895*^9}, {3.49870956871157*^9, 3.498709571670253*^9}},
 CellID->1992168876],

Cell[BoxData[
 RowBox[{
  RowBox[{"exampleCoords", "=", 
   RowBox[{"LoadLattice", "[", 
    RowBox[{"\"\<Diamond\>\"", ",", "$DiamondLatticeConst", ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], "]"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.498643262970081*^9, 3.498643267521884*^9}},
 CellLabel->"In[24]:=",
 CellID->1653152907],

Cell[BoxData[
 RowBox[{
  RowBox[{"exampleBath", "=", 
   RowBox[{"GenerateBath", "[", 
    RowBox[{"exampleCoords", ",", "$DiamondNatureAbundance", ",", "1"}], 
    "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.498643285061036*^9, 3.498643312423455*^9}, {
   3.49864341236275*^9, 3.498643415464169*^9}, {3.498694875193352*^9, 
   3.49869487927407*^9}, 3.498709597446375*^9},
 CellLabel->"In[25]:=",
 CellID->1354900819],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"DipolarInteractionTable", "[", 
   RowBox[{"exampleBath", ",", "0.0300", ",", 
    RowBox[{"0.0", "Degree"}], ",", 
    RowBox[{"0.0", "Degree"}], ",", 
    RowBox[{"Table", "[", 
     RowBox[{"$GammaC13", ",", 
      RowBox[{"{", 
       RowBox[{"Length", "[", "exampleBath", "]"}], "}"}]}], "]"}], ",", 
    "3"}], "]"}], "//", "TableForm"}]], "Input",
 CellLabel->"In[26]:=",
 CellID->902292725],

Cell[BoxData[
 TagBox[GridBox[{
    {"0.`", 
     RowBox[{"-", "0.010210396373315117`"}], "2.9658521334019508`", 
     "0.12054283580826236`", 
     RowBox[{"-", "0.031564118778749144`"}], 
     RowBox[{"-", "0.08670957029441628`"}], "0.006643508778820368`", 
     "0.02065034761399272`", "0.0160747141284141`"},
    {
     RowBox[{"-", "0.010210396373315117`"}], "0.`", "0.0018848009521772293`", 
     "0.00907987545439491`", 
     RowBox[{"-", "0.9512975153312461`"}], 
     RowBox[{"-", "0.012369434263150106`"}], 
     RowBox[{"-", "0.031456260522627996`"}], "0.02073281047394952`", 
     "0.0012277236976850452`"},
    {"2.9658521334019508`", "0.0018848009521772293`", "0.`", 
     "0.05394419614895935`", 
     RowBox[{"-", "0.02065034761399273`"}], 
     RowBox[{"-", "0.032116934783279406`"}], "0.007046648261712928`", 
     "0.024549870161249317`", "0.0100291057959058`"},
    {"0.12054283580826236`", "0.00907987545439491`", "0.05394419614895935`", 
     "0.`", 
     RowBox[{"-", "0.007395931103151722`"}], 
     RowBox[{"-", "0.11891218941640577`"}], "0.005256861523431355`", 
     "0.006690603221484772`", "0.0560692736569347`"},
    {
     RowBox[{"-", "0.031564118778749144`"}], 
     RowBox[{"-", "0.9512975153312461`"}], 
     RowBox[{"-", "0.02065034761399273`"}], 
     RowBox[{"-", "0.007395931103151722`"}], "0.`", 
     RowBox[{"-", "0.009220974159746462`"}], 
     RowBox[{"-", "0.01586316600001708`"}], 
     RowBox[{"-", "0.006643508778820381`"}], 
     RowBox[{"-", "0.0033530756311445434`"}]},
    {
     RowBox[{"-", "0.08670957029441628`"}], 
     RowBox[{"-", "0.012369434263150106`"}], 
     RowBox[{"-", "0.032116934783279406`"}], 
     RowBox[{"-", "0.11891218941640577`"}], 
     RowBox[{"-", "0.009220974159746462`"}], "0.`", "0.018844140168714375`", 
     "0.0014570647015677918`", "0.008775345082939125`"},
    {"0.006643508778820368`", 
     RowBox[{"-", "0.031456260522627996`"}], "0.007046648261712928`", 
     "0.005256861523431355`", 
     RowBox[{"-", "0.01586316600001708`"}], "0.018844140168714375`", "0.`", 
     RowBox[{"-", "0.03733519728062199`"}], "0.007235076900665198`"},
    {"0.02065034761399272`", "0.02073281047394952`", "0.024549870161249317`", 
     "0.006690603221484772`", 
     RowBox[{"-", "0.006643508778820381`"}], "0.0014570647015677918`", 
     RowBox[{"-", "0.03733519728062199`"}], "0.`", "0.0035441780156231983`"},
    {"0.0160747141284141`", "0.0012277236976850452`", "0.0100291057959058`", 
     "0.0560692736569347`", 
     RowBox[{"-", "0.0033530756311445434`"}], "0.008775345082939125`", 
     "0.007235076900665198`", "0.0035441780156231983`", "0.`"}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.7]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.498709602018297*^9},
 CellLabel->"Out[26]//TableForm=",
 CellID->1790133427]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["More About", "TutorialMoreAboutSection",
 CellID->23220180],

Cell[TextData[ButtonBox["Magnetic Resonance",
 BaseStyle->"Link",
 ButtonData->"paclet:MathMR/guide/Magnetic Resonance"]], "TutorialMoreAbout",
 CellChangeTimes->{{3.49870479349109*^9, 3.498704806170119*^9}},
 CellID->238287387]
}, Open  ]],

Cell[CellGroupData[{

Cell["Related Tutorials", "RelatedTutorialsSection",
 CellID->415694126],

Cell["XXXX", "RelatedTutorials",
 CellID->806871991]
}, Open  ]],

Cell[CellGroupData[{

Cell["Related Wolfram Education Group Courses", "TutorialRelatedLinksSection",
 CellID->415694148],

Cell["XXXX", "TutorialRelatedLinks",
 CellID->415694149]
}, Open  ]]
}, Open  ]]
},
WindowSize->{700, 770},
WindowMargins->{{Automatic, 320}, {Automatic, 25}},
FrontEndVersion->"7.0 for Linux x86 (32-bit) (February 25, 2009)",
StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "TutorialPageStyles.nb", 
  CharacterEncoding -> "iso8859-1"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[545, 20, 325, 14, 26, "History",
 CellID->1247902091],
Cell[CellGroupData[{
Cell[895, 38, 68, 1, 30, "CategorizationSection",
 CellID->1122911449],
Cell[966, 41, 81, 2, 70, "Categorization",
 CellID->686433507],
Cell[1050, 45, 79, 2, 70, "Categorization",
 CellID->605800465],
Cell[1132, 49, 76, 2, 70, "Categorization",
 CellID->468444828],
Cell[1211, 53, 74, 1, 70, "Categorization"]
}, Closed]],
Cell[CellGroupData[{
Cell[1322, 59, 56, 1, 20, "KeywordsSection",
 CellID->1427428552],
Cell[1381, 62, 45, 1, 70, "Keywords",
 CellID->1251852827]
}, Closed]],
Cell[CellGroupData[{
Cell[1463, 68, 53, 1, 20, "DetailsSection",
 CellID->307771771],
Cell[1519, 71, 63, 2, 70, "Details",
 CellID->218895918],
Cell[1585, 75, 69, 2, 70, "Details",
 CellID->350963985],
Cell[1657, 79, 66, 2, 70, "Details",
 CellID->795871300],
Cell[1726, 83, 71, 2, 70, "Details",
 CellID->199739161],
Cell[1800, 87, 60, 2, 70, "Details",
 CellID->40625308],
Cell[1863, 91, 61, 2, 70, "Details",
 CellID->357121918],
Cell[1927, 95, 62, 2, 70, "Details",
 CellID->35949532],
Cell[1992, 99, 78, 2, 70, "Details",
 CellID->929432370],
Cell[2073, 103, 67, 2, 70, "Details",
 CellID->240026365]
}, Closed]],
Cell[CellGroupData[{
Cell[2177, 110, 50, 1, 106, "Title",
 CellID->509267359],
Cell[2230, 113, 192, 5, 24, "Text",
 CellID->1534169418],
Cell[2425, 120, 858, 23, 108, "DefinitionBox",
 CellID->2096742444],
Cell[3286, 145, 123, 2, 30, "Caption",
 CellID->1891092685],
Cell[CellGroupData[{
Cell[3434, 151, 204, 5, 57, "MathCaption",
 CellID->836781195],
Cell[CellGroupData[{
Cell[3663, 160, 197, 5, 28, "Input",
 CellID->201251739],
Cell[3863, 167, 370, 11, 26, "Output",
 CellID->1297040926]
}, Open  ]],
Cell[CellGroupData[{
Cell[4270, 183, 204, 5, 28, "Input",
 CellID->1686696713],
Cell[4477, 190, 712, 29, 55, "Output",
 CellID->1379868343]
}, Open  ]],
Cell[CellGroupData[{
Cell[5226, 224, 248, 7, 28, "Input",
 CellID->1089850160],
Cell[5477, 233, 620, 16, 47, "Output",
 CellID->2143837741]
}, Open  ]]
}, Open  ]],
Cell[6124, 253, 1173, 32, 144, "DefinitionBox",
 CellID->295055199],
Cell[7300, 287, 126, 2, 30, "Caption",
 CellID->879203334],
Cell[CellGroupData[{
Cell[7451, 293, 254, 6, 57, "MathCaption",
 CellID->874840856],
Cell[CellGroupData[{
Cell[7730, 303, 298, 8, 28, "Input",
 CellID->723392520],
Cell[8031, 313, 1290, 34, 58, "Output",
 CellID->303982011]
}, Open  ]],
Cell[CellGroupData[{
Cell[9358, 352, 321, 9, 28, "Input",
 CellID->1141463959],
Cell[9682, 363, 1295, 34, 58, "Output",
 CellID->285172659]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[11026, 403, 226, 4, 40, "MathCaption",
 CellID->1520014403],
Cell[CellGroupData[{
Cell[11277, 411, 235, 7, 28, "Input",
 CellID->1940946482],
Cell[11515, 420, 1973, 47, 114, "Output",
 CellID->706670819]
}, Open  ]],
Cell[CellGroupData[{
Cell[13525, 472, 283, 7, 28, "Input",
 CellID->1668430510],
Cell[13811, 481, 1971, 48, 114, "Output",
 CellID->729389960]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[15831, 535, 303, 4, 40, "MathCaption",
 CellID->857902880],
Cell[CellGroupData[{
Cell[16159, 543, 270, 7, 28, "Input",
 CellID->2042472293],
Cell[16432, 552, 264, 7, 26, "Output",
 CellID->1551133660]
}, Open  ]]
}, Open  ]],
Cell[16723, 563, 1138, 28, 94, "DefinitionBox",
 CellID->609356121],
Cell[17864, 593, 182, 3, 30, "Caption",
 CellID->1087339240],
Cell[CellGroupData[{
Cell[18071, 600, 328, 5, 40, "MathCaption",
 CellID->1883277671],
Cell[CellGroupData[{
Cell[18424, 609, 439, 12, 51, "Input",
 CellID->1101951984],
Cell[18866, 623, 284, 7, 26, "Output",
 CellID->816580272]
}, Open  ]],
Cell[CellGroupData[{
Cell[19187, 635, 576, 16, 73, "Input",
 CellID->2026486792],
Cell[19766, 653, 262, 7, 26, "Output",
 CellID->1963445781]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[20077, 666, 397, 6, 40, "MathCaption",
 CellID->42218018],
Cell[CellGroupData[{
Cell[20499, 676, 653, 20, 73, "Input",
 CellID->154343777],
Cell[21155, 698, 359, 8, 28, "Output",
 CellID->104243093]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[21563, 712, 443, 6, 40, "MathCaption",
 CellID->1992168876],
Cell[22009, 720, 609, 19, 51, "Input",
 CellID->1653152907],
Cell[22621, 741, 422, 10, 28, "Input",
 CellID->1354900819],
Cell[CellGroupData[{
Cell[23068, 755, 433, 12, 51, "Input",
 CellID->902292725],
Cell[23504, 769, 3179, 69, 151, "Output",
 CellID->1790133427]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[26732, 844, 65, 1, 74, "TutorialMoreAboutSection",
 CellID->23220180],
Cell[26800, 847, 228, 4, 23, "TutorialMoreAbout",
 CellID->238287387]
}, Open  ]],
Cell[CellGroupData[{
Cell[27065, 856, 72, 1, 74, "RelatedTutorialsSection",
 CellID->415694126],
Cell[27140, 859, 52, 1, 23, "RelatedTutorials",
 CellID->806871991]
}, Open  ]],
Cell[CellGroupData[{
Cell[27229, 865, 98, 1, 74, "TutorialRelatedLinksSection",
 CellID->415694148],
Cell[27330, 868, 56, 1, 23, "TutorialRelatedLinks",
 CellID->415694149]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
